1)Can a person working in company A in L1 Blanket visa move to company B if company B is ready to sponsor the H1B?
No. You need to have the H-1B status in order to work for B.
2) What are the exact steps the company B needs to take for this process?
The same ones it would take for a normal H-1B.
You should retain an experienced immigration lawyer to review all the facts and advise you accordingly.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.